Asymptotic analysis of the closed network with time-dependent service parameters and single-type messages

A queueing network of any structure with single-type messages is considered in the paper. An asymptotic analysis of the network in case of large number of service requests conducted. It is suggested that the service parameters of each queueing system of the network, as well as the probability of messages transition between systems, depend on time. A system of ordinary differential equations to calculate the average relative number of messages in each queueing system, depending on the time, was obtained. There is one calculated example in the article.